Journal of Business Economics

, Volume 83, Issue 1, pp 29–60 | Cite as

Beyond Markowitz with multiple criteria decision aiding

  • Salvatore Greco
  • Benedetto Matarazzo
  • Roman Słowiński
Original Paper

Abstract

The paper is about portfolio selection in a non-Markowitz way, involving uncertainty modeling in terms of a series of meaningful quantiles of probabilistic distributions. Considering the quantiles as evaluation criteria of the portfolios leads to a multiobjective optimization problem which needs to be solved using a Multiple Criteria Decision Aiding (MCDA) method. The primary method we propose for solving this problem is an Interactive Multiobjective Optimization (IMO) method based on so-called Dominance-based Rough Set Approach (DRSA). IMO-DRSA is composed of two phases: computation phase, and dialogue phase. In the computation phase, a sample of feasible portfolio solutions is calculated and presented to the Decision Maker (DM). In the dialogue phase, the DM indicates portfolio solutions which are relatively attractive in a given sample; this binary classification of sample portfolios into ‘good’ and ‘others’ is an input preference information to be analyzed using DRSA; DRSA is producing decision rules relating conditions on particular quantiles with the qualification of supporting portfolios as ‘good’; a rule that best fits the current DM’s preferences is chosen to constrain the previous multiobjective optimization in order to compute a new sample in the next computation phase; in this way, the computation phase yields a new sample including better portfolios, and the procedure loops a necessary number of times to end with the most preferred portfolio. We compare IMO-DRSA with two representative MCDA methods based on traditional preference models: value function (UTA method) and outranking relation (ELECTRE IS method). The comparison, which is of methodological nature, is illustrated by a didactic example.

Keywords

Portfolio selection Uncertainty modeling Multiple criteria decision aiding Interactive multiobjective optimization Dominance-based rough set approach 

JEL Classification

C61 C63 G11 

Notes

Acknowledgements

The third author wishes to acknowledge financial support from the Polish National Science Centre, grant no. NN519 441939.

References

  1. Acerbi C (2002) Spectral measures of risk: a coherent representation of subjective risk aversion. J Bank Financ 26(7):1505–1518CrossRefGoogle Scholar
  2. Acerbi C, Tasche D (2002) Expected shortfall: a natural coherent alternative to value at risk. Econ Notes 31:379–388CrossRefGoogle Scholar
  3. Artzner Ph, Delbaen F, Eber JM, Heath D (1999) Coherent measures of risk. Math Financ 9(3):203–228CrossRefGoogle Scholar
  4. Belton V, Branke J, Eskelinen P, Greco S, Molina J, Ruiz F, Słowiński R (2008) Interactive multiobjective optimization from a learning perspective, chapter 15. In: Branke J, Deb K, Miettinen K, Słowiński R (eds) Multiobjective optimization: interactive and evolutionary approaches. LNCS vol 5252, state-of-the-art surveys. Springer, Berlin, pp 405–434Google Scholar
  5. Bigelow JP (1993) Consistency of mean-variance analysis and expected utility analysis: a complete characterisation. Econ Lett 43:187–192CrossRefGoogle Scholar
  6. Blaszczyński J, Słowiński R, Szelag J (2011) Sequential covering rule induction algorithm for variable consistency rough set approaches. Inf Sci 181:987–1002CrossRefGoogle Scholar
  7. Branke J, Deb K, Miettinen K, Słowiński R (eds) (2008) Multiobjective optimization: interactive and evolutionary approaches. In: LNCS, vol 5252, state-of-the-art surveys. Springer, BerlinGoogle Scholar
  8. Choquet G (1953–1954). Theory of capacities. Ann Inst Fourier 5:131–295Google Scholar
  9. Corrente S, Greco S, Słowiński R (2012) Multiple criteria hierarchy process in robust ordinal regression. Decis Support Syst 53:660–674CrossRefGoogle Scholar
  10. Corrente S, Greco S, Słowiński R (2013) Multiple criteria hierarchy process with ELECTRE and PROMETHEE. Omega 41:820–846Google Scholar
  11. Dybvig PH, Ingersoll JE (1982) Mean-variance theory in complete markets. J Business 55:233–251CrossRefGoogle Scholar
  12. Dyer JS (2005) MAUT-multiattribute utility theory, chapter 7. In: Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: state-of-the-art surveys. Springer, New York, pp 265–295Google Scholar
  13. Elton EJ, Gruber MJ (1995) Modern portfolio theory and investment analysis. Wiley, New YorkGoogle Scholar
  14. Fama E (1963) Mandelbrot and the stable Paretian hypothesis. J Business 36:420–429CrossRefGoogle Scholar
  15. Fama E (1965a) The behavior of stock market prices. J Business 38:34–105CrossRefGoogle Scholar
  16. Fama E (1965b) Portfolio analysis in a stable Paretian market. Manage Sci 11:404–419CrossRefGoogle Scholar
  17. Figueira J, Greco S, Ehrgott M (eds) (2005) Multiple criteria decision analysis, state-of-the-art surveys. Springer, New YorkGoogle Scholar
  18. Figueira J, Greco S, Roy B (2009) ELECTRE methods with interaction between criteria: an extension of the concordance index. Eur J Oper Res 199:478–495CrossRefGoogle Scholar
  19. Figueira J, Greco S, Słowiński R (2009) Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method. Eur J Oper Res 195:460–486CrossRefGoogle Scholar
  20. Figueira J, Mousseau V, Roy B (2005) ELECTRE methods, chapter 14. In: Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: state-of-the-art surveys. Springer, New York, pp 133–162Google Scholar
  21. Grabisch M, Labreuche Ch (2005) Fuzzy measures and integrals in MCDA, chapter 5. In: Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: state-of-the-art surveys, Springer, New York, pp 563–608Google Scholar
  22. Greco S, Kadziński M, Mousseau V, Słowiński R (2011) ELECTREGKMS: robust ordinal regression for outranking methods. Eur J Oper Res 214:118–135CrossRefGoogle Scholar
  23. Greco S, Matarazzo B, Słowiński R (2001a) Rough sets theory for multicriteria decision analysis. Eur J Oper Res 129:1–47Google Scholar
  24. Greco S, Matarazzo B, Słowiński R, Stefanowski J (2001b) An algorithm for induction of decision rules consistent with dominance principle. In: Ziarko W, Yao Y (eds) Rough sets and current trends in computing. LNAI, vol 2005. Springer, Berlin, pp 304–313Google Scholar
  25. Greco S, Matarazzo B, Słowiński R (2005) Decision rule approach, chapter 13. In: Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: state-of-the-art surveys. Springer, New York, pp 507–562Google Scholar
  26. Greco S, Matarazzo B, Słowiński R (2008a) Dominance-based rough set approach to interactive multiobjective optimization, chapter 5. In: Branke J, Deb K, Miettinen K, Słowiński R (eds) Multiobjective optimization: interactive and evolutionary approaches. LNCS, vol 5252, State-of-the-Art Surveys. Springer, Berlin, pp 121–155Google Scholar
  27. Greco S, Mousseau V, Słowiński R (2008b) Ordinal regression revisited: multiple criteria ranking using a set of additive value functions. Eur J Oper Res 191:415–435Google Scholar
  28. Greco S, Matarazzo B, Słowiński R (2010) Dominance-based rough set approach to decision under uncertainty and time preference. Ann Oper Res 176:41–75CrossRefGoogle Scholar
  29. Greco S, Matarazzo B, Słowiński R, Vaccarella G (2012a) Inventory control using interactive multiobjective optimization guided by dominance-based rough set approach (submitted)Google Scholar
  30. Greco S, Mousseau V, Słowiński R (2012b) UTAGMS − INT: robust ordinal regression for value functions handling interacting criteria (submitted)Google Scholar
  31. Greco S, Słowiński R, Zielniewicz P (2013) Putting dominance-based rough set approach and robust ordinal regression together. Decis Support Syst 54:891–903Google Scholar
  32. Jacquet-Lagrèze E, Siskos Y (1982) Assessing a set of additive utility functions for multicriteria decision making: the UTA method. Eur J Oper Res 10:151–164CrossRefGoogle Scholar
  33. Jarrow RA, Madan DB (1997) Is mean-variance analysis vacuous: or was beta still born? Eur Finance Rev 1:15–30CrossRefGoogle Scholar
  34. Jorion Ph (2006) Value at risk: the new benchmark for managing financial risk, 3rd edn. McGraw Hill, New YorkGoogle Scholar
  35. Keeney RL, Raiffa H (1976) Decisions with multiple objectives: preferences and value tradeoffs. Wiley, New YorkGoogle Scholar
  36. Lintner J (1965) The valuation of risky assets and the selection of risky investments in stock portfolios and capital budget. Rev Econ Stat 47:13–37CrossRefGoogle Scholar
  37. Maccheroni F, Marinacci M, Rustichini A, Taboga M (2009) Portfolio selection with monotone mean-variance preferences. Math Financ 19(3):487–521CrossRefGoogle Scholar
  38. Mandelbrot B (1963) The variation of certain speculative prices. J Bus 36(4):394–419CrossRefGoogle Scholar
  39. Mandelbrot B (1967) The variation of some other speculative prices. J Bus 40:393–413CrossRefGoogle Scholar
  40. Markowitz HM (1952) Portfolio selection. J Financ 7:77–91Google Scholar
  41. Markowitz HM (1959) Portfolio selection: efficient diversification of investments. Wiley/Yale University Press, 1970, Basil/Blackwell, 1991Google Scholar
  42. Matos MA (2006) Decision under risk as a multicriteria problem. Eur J Oper Res 181:1516–1529CrossRefGoogle Scholar
  43. Mossin J (1966) Equilibrium in a capital asset market. Econometrica 34:768–783CrossRefGoogle Scholar
  44. Pawlak Z (1991) Rough sets. Theoretical aspects of reasoning about data. Kluwer, DordrechtGoogle Scholar
  45. Rachev S, Ortobelli S, Schwartz E (2004) The problem of optimal asset allocation with stable distributed returns. In: Krinik A, Swift R (eds) Stochastic processes and functional analysis: a volume of recent advances in honor of M.M. Rao. Lecture notes in pure and applied mathematics. Marcel Dekker, New York, pp 295–347Google Scholar
  46. Rockafellar RT, Uryasev SP (2000) Optimization of conditional value-at-risk. J Risk 2:21–42Google Scholar
  47. Ross S (1976) The arbitrage theory of capital pricing. J Econ Theory 13:341–360CrossRefGoogle Scholar
  48. Roy B (1968) Classement et choix en présence de points de vue multiples (la méthode ELECTRE). RIRO 8:57–75Google Scholar
  49. Roy B (1991) The outranking approach and the foundations of ELECTRE methods. Theor Decis 31:49–73CrossRefGoogle Scholar
  50. Roy B, Skalka J (1984) ELECTRE IS: Aspects méthodologiques et guide d’utilisation. Document du LAMSADE 30, Université Paris Dauphine, ParisGoogle Scholar
  51. Roy B, Vincke Ph (1984) Relational systems of preference with one or more pseudo-criteria: some new concepts and results. Manage Sci 30:1323–1335CrossRefGoogle Scholar
  52. Sharpe WF (1963) A simplified model for portfolio analysis. Manage Sci 9:277–293CrossRefGoogle Scholar
  53. Sharpe WF (1964) Capital asset prices: a theory of market equilibrium under conditions of risk. J Financ 19:425–442Google Scholar
  54. Słowiński R, Greco S, Matarazzo B (2005) Rough set based decision support, chapter 16. In: Burke EK, Kendall G (eds), Search methodologies: introductory tutorials in optimization and decision support techniques. Springer, New York, pp 475–527Google Scholar
  55. Słowiński R, Greco S, Matarazzo B (2009) Rough sets in decision making. In: Meyers RA (ed) Encyclopedia of complexity and systems science. Springer, New York, pp 7753–7786Google Scholar
  56. Słowiński R, Greco S, Matarazzo B (2012) Rough set and rule-based multicriteria decision aiding. Pesqui Oper 32:213–269CrossRefGoogle Scholar
  57. Spronk J, Steuer RE, Zopounidis C (2005) Multicriteria decision analysis/aid in finance, chapter 20. In: Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: state-of-the-art surveys. Springer, New York, pp 799–857Google Scholar
  58. Steuer RE, Na P (2003) Multiple criteria decision making combined with finance: a categorized bibliography. Eur J Oper Res 150:496–515CrossRefGoogle Scholar
  59. Steuer RE, Qi Y, Hirschberger M (2005) Multiple objectives in portfolio selection. J Financ Decis Mak 1:5–20Google Scholar
  60. Tversky A, Kahnemann D (1992) Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncertain 5(4):297–323CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Salvatore Greco
    • 1
  • Benedetto Matarazzo
    • 1
  • Roman Słowiński
    • 2
    • 3
  1. 1.Department of Economics and BusinessUniversity of CataniaCataniaItaly
  2. 2.Institute of Computing SciencePoznań University of TechnologyPoznanPoland
  3. 3.Systems Research InstitutePolish Academy of SciencesWarsawPoland

Personalised recommendations